As a student you are able to register at home and at your term-time address. So wherever you are on election day, you can have your say.
There are other good reasons to register; the main one being that if you are not on the register of electors you may experience problems obtaining credit as the register is used by credit reference agencies to confirm your address.
So not being registered could mean you may struggle to get a new mobile phone contract, open a bank account and possibly later in life a mortgage.
You need to register to be allowed to vote in elections and referendums. The way you register changed in 2014 and since then:
You can't vote twice in a UK Parliamentary, Scottish Parliamentary, National Assembly for Wales or European Parliamentary election. You would be committing an offence if you voted twice. However, you can vote in a local government election at home and at your term-time address, as long as they are in different local government areas.