At its simplest, terrorism can be defined as a form of political violence that achieves it's aims through creating a climate of fear and apprehension. The very nature of terrorism is fluid and difficult to pinpoint with one definition, however, terrorism is usually a clandestine act of violence that attacks innocent civilians and the perpetrators are often non-state actors attempting to influence a government. The nature of terrorism has indeed transformed particularly since the 9/11 attacks (although some argue earlier than this, e.g. the 1995 Tokyo subway attack), the key transformation being the shift from away from secular traditional political terrorism (i.e the IRA) to religiously motivated terror.
The significance of this 'new' terrorism lies largely in it's global character. The advent of globalisation has, arguably, allowed for terrorism to develop onto the international stage. Hyper-mobility in terms of cross-border flows of people, good, money, ideas, etc. has been exploited by terrorists groups. Increased migration flows has helped sustain terrorist campaigns as diaspora communities can be a key source of funding such as the Tamil Tigers (however, this concept is not entirely modern and can be traced back to the 19th century Fenian movement in America). Furthermore, aside from making the process of terrorism easier, globalisation has also generated pressures that can be seen as causing terrorism. For instance, cultural globalisation is often seen as Westerenisation which generates a backlash from those who do not align themselves to western values. Perhaps most significant of all is the fact that globalisation causes huge imbalances as the soul-sucking global capitalist system spreads and impoverishes those most vulnerable to terrorist recruitment.
Perhaps the most notable form of modern terrorism, Islamist, has been the most successful in achieving a global reach. This is largely due to the failings of political islam in the late 1990s, and so domestic jihad was replaced by a global jihad as the islamist movment united around the 'far enemy': western policy. Al-Qaeda are a prominent example of this, their goals are transnational and, to an extent, civilisational (although ISIS is a better example to demonstrate a civilisational attack). Therefore, not only can this new form of terrorism strike anytime and anywhere, by realigning it's targets to a civilisation it greatly increases the number of potential targets.
As well as acquiring a global reach, another key significance of 'new' international terrorism is the catastrophic threat it poses. 9/11 is often seen as the most costly terrorist attack in history with roughly 3,000 deaths, the psychological impact it caused was devastating, denting the old myth that America was invulnerable. However, the significance of the attack is not in the number of casualties (for, when compared to conventional warfare e.g. 1.5 million killed in the Somme, it is relatively small), The significance is that it highlighted an intractable security threat, something which has the potential to wreak utter death and destruction- something which is near impossible to protect against.
There are other reasons why new international terrorism poses such a threat. Firstly, terrorism is a form of gurellia warfare and as such it is difficult to distinguish who is an innocent civilian and who is a terrorist. It is often carried out by lone individuals or small groups, e.g. suicide bombings- it has proven extremely difficult to provide protection against attackers who are willing to sacrifice their lives to promote their cause. Perhaps it is possible to reduce the likelihood of terror attacks, but we are never going to see the threat of terror be eradicated completely.
Additionally, the potential devastation of terrorism has increased due to easier access to modern technology, particular WMD. Nuclear proliferation has run the risk of terrorists acquiring such weapons, Allison (2004) argued that a nuclear terrorist attack on the USA was inevitable unless some form of lock down on nuclear materials on a global scale was reached. Not only do terrorists have an easier access to WMD, they are far more likely to use them due to the moral context of their motivations. For instance, radical politico-religious Islamist terrorism views the west as inherently corrupt and an intrinsic enemy of Islam itself, and therefore would have few scruples in using such weapons to eradicate this perceived 'evil'.
However, the significance of international terrorism does run the risk of being overstated. Firstly, if we look to the jihadist movement as the prominent example of international terrorism, it is by far a united force. The attacks we have seen (9/11, Madrid, London) are not linked by common inspiration or unified purpose. Some argue these terrorists are not global revolutionaries but rather religious nationalists.
Also, the military threat of international terrorism is relatively small. Due to its nature of sporadic attacks on a variety of targets, it is less damaging than most conventional sustained inter-state warfare. Addtionally, terrorism in itself cannot overthrow a government, it is the governments response to the fear that decides the course of action.
Furthermore, the concept of Islamist terrorism as global terrorism stems less from the nature of the terrorism and more so because of the response. The 'war on terror' is largely an ideological construct. Now that the threat of communism is exhausted, the US need a new threat to maintain its hegemonic position, particularly in the Middle East (it's all about oil). In doing so it justifies it's actions by indoctrinating the masses into an "us VS them" mentality.