There are several ways that someone may have your credit/debit card details and I will try to list them.
1) Trojan - One of them which was mentioned already is via a trojan horse virus which can be in the form of screen capture or keylogger which then sends back the data to a remote server. A good antivirus software should detect if you have this.
2) Phishing - Again previously mentioned, accidentally entering your details into a fake website would result in your card details stolen. This is why some websites have the HTTPS on their URL that proves who they are from a Certification Company or CA.
3) Unsecured communication - For instance, sending card details over an unencrypted connection (HTTPS or TLS) or stating your card details over the phone; something which I never do as phone companies can listen for line quality.
4) Social Engineering - Where trust is gained from the outside and the attacker gains valuable information by simulating a trusted agent.
5) Dumpster Diving - As the name implies - get a good quality shredder or burn your important documents
6) Injections - These are very common and happen all the time, as my lecturer said, no system is safe. What is done is actually trying to limit the damage if someone gets in; imagine like a castle and you place traps to stop invaders from getting in.
This largely depends on how much the company invests in security and patching up on their servers with up to date software that runs their systems and has no vulnerabilities. One example that comes to mind was a script kiddie (think of a pyramid and these are plentiful unskilled hackers that steal code from the professional hackers from the top) hacking Talk Talk and publishing their details online which made the news on national TV. SQL injections were used and these are simple SELECT * FROM x SQL statements using a parameter on the URL via GET method. Suppose if the attacker does acquire one way encrypted card details using alphanumeric sets. The attacker would need to use brute force methods to go through billions of combinations to get through all possible combinations which takes several years at the current rate which processors can carry out processes. This is why cards have an expiry limitation of around 4 years.
7) Cloned cards - Sliding your card unwittingly in an ATM card reader where your card details have been copied and used by the attacker.
Other methods exists and these are the ones at the top of my head so there could be other reasons why those payments have appeared but if you suspect anything, just tell your bank to cancel the card and flag those payments as suspect.