A reserve requirement says the following: Sum up the amount of deposits of a bank (on the passive, debt side of the balance sheet), call that A. Then look at what the bank has in its account(s) at the central bank, call that B. Banks must ensure that on average, B must be greater than x% of A.
So, let's look at a simple example of a bank B that fulfills its reserve requirements exactly at the beginning of this story.
Let's say some client, C, receives an electronic transfer from somebody at a different bank to the amount of 100#. The bank updates their database to increase the number that C sees on their bank statement.
Around the same time, the sending bank S also makes an electronic transfer of central bank money of 100#. This typically goes indirectly via a clearing system, but in practice we can pretend that both banks have an account at the central bank, and central bank money is transferred between those accounts by the central bank updating its database. [0]
At the end of the transaction, bank B's liabilities have increased by 100# (more deposits), and so have its assets (more money in its central bank account).
Moreover, while B has gained 100# in central bank money, its reserve requirement has only grown by 1#, assuming a 1% reserve requirement. This means that according to the reserve requirement, bank B is allowed to have an additional 9900# in deposits.
One way that the bank can leverage this is to hand out a 9900# loan. Let us assume that it does so. That is, it gives some client a deposit of 9900#. Now the reserve requirement is fulfilled precisely again.
You will now probably think, well, the client is going to do something with those 9900#. True, and it becomes relevant if the client transfers this money to somebody whose account is with another bank (otherwise, everything happens locally to one bank and the reserve requirement does not matter).
In that base, bank B will have to send 9900# of central bank money to the receiving bank. However, it's reserve requirement is reduced only by 99#, so it will be 9801# short. Oops. Did the bank break the law?
No, because they are only required to fulfil the reserve requirement within a specified amount of time! During this time, the bank's interbank market traders will simply borrow the required amount of central bank money from another bank, using the bank's assets as security.
Most of the times even this is unnecessary [1], because other banks also make loans, and electronic transfers between banks cancel out.
Initially, this may now look as if the banking system as a whole could just create loans absolutely at will - and that is actually largely true. However, there are some limitations.
However, reserve requirements are not a limitation. If you think the above through, you might come to the conclusion that the banking system as a whole might at some point not have enough central bank money to satisfy the reserve requirements. However, this can never happen because of the central bank's mandate for interest rate stability.
What happens when the banking system as a whole creates a huge number of loans is that bidding in the interbank market would drive up the interest rate for short term central bank money. However, the central bank has a fixed target for this interest rate and will therefore lend out central bank money to the banks (thereby increasing the monetary base) to calm the bidding. [2]
The true limitation of bank lending comes from capital requirements, and for good reasons. When a loan defaults, this hits the banks profits, and when a bank makes losses, they hit the bank's capital - which is morally and capitalistically okay. Loss of capital is exactly what should happen when a bank makes bad lending decisions. So society requires a buffer of capital that is large enough relative to the amount of loans (not deposits!) that a bank has made. Naturally, the size of this buffer is a hotly debated topic, because the larger the buffer, the better for stability, but the smaller the buffer, the better for the bankers.
[0] This is simply a description of how inter-bank money transfers work, and really should be part of every school curriculum. I bet a clear majority of people has never even thought about how any of this works, even though it is a foundational fact about how our society functions.
[1] Actually, it is still necessary due to fluctuations, but the flows involved are much smaller.
[2] This is describing the "normal" situation outside of the liquidity trap scenario we are currently living in. It is important to note that in what I described, the expansion of the monetary base is not a decision of the central bank. It is endogenously driven by the commercial banks' lending decisions.