You understood it pretty right.
Every fiscal year (which runs from April 6 year Y to April 5 year Y+1), you can deposit a total GBP15k (this number is subject to an annual increase by HMRC) into your ISAs. You can open 2 new ISA every year but the amount deposited to those ISAs shall not excess GBP15k in total.
From the 2016/17 tax year some ISAs now permit you to replace any funds you have withdrawn, without using up your allowance. It used to be that if you deposited GBP15K and then withdrew GBP5K, you could not pay in to that ISA again within that tax year as you had already used your full allowance. Under new Flexible ISA rules this would be allowed providing you replace the funds in the same ISA account and within the same tax year (strongly recommend that you check the small prints related to your account to make sure this is he case).
Any gains and losses on the investments held in the ISA accounts are for you to take. i.e. If you make investment gains of GBP5K this does not reduces your allowance. You will still be able to deposit GBP15k (or whatever HMRC increases that number to) in the following year.
You are also allowed to consolidate your ISAs. You can ask bank A to transfer the amount held into an ISA with bank held with bank B. This is usually done by filling a special form with the bank that will held the money post transactions. Again here be very careful. DO NOT withdraw the money to transfer it yourself as this would count against the GBP15K limit. Instead follow the procedures from the bank.
Finally if you don't use your allowance for a given year, you cannot use it during the following year. i.e. if you don't deposit the GBP15K this year, then you cannot deposit GBP30K next year.
NB: I used the word "deposit". It does not matter to HMRC if the money get invested or not. If you are in a rush on April 4th, just make sure the money is wired into the ISA account by the 5th. No need to rush and make bad investment decision. You can invest it later.
Hope it helps