Unfortunately terrorism has no universal definition which presents problems in many areas. Yet many high education institutions and governments do share a similar definition: (converted to my own words) an act of violence committed on civilians perpetrated in order to influence government policy.
now through this definition and historical episodes we can see religion has no part in the theory of terrorism. However, the practice of terrorism does tend to have strong religious roots today.

Terrorism is a constantly changing phenomenon played out with different tactics, means, targets and 'battle grounds'. it is constantly evolving. unfortunately there is no single definition accepted globally which presents huge problems. but we wont go into that.
there are various parties who benefit from terror. firstly and obviously the terrorists directly involved. they have a set goal and achieve it. as stated above- it is a political tool aimed at terrorizing- instilling fear into society so as to change the agenda in the long/short run. so with each attack, as public reaction experiences fright, hesitation and self questioning; the goal of the terrorist has been achieved.
secondly, the supporters of terrorists. yes- each group has many supporters who do not and will not engage in terrorism physically. they prefer to sponsor, promote and believe in the particular terrorist group's ideology. as they see their 'brothers' achieve mass casualties, public fright and media attention they benefit believing their political ideology is catching on and that change may occur in the future.
the monetary beneficiaries are endless: weapon manufactures, arms dealers, transport services, lodging havens, passport forgers, bomb makers. They do not have to belong to a terrorist group or even side with them ideologically- money rules largely with this group in many cases. large terrorist organisations can have a significant impact on a local economy e.g. hezbollah and al qaede.