Processors give the illusion of a sequence of instructions executed one-by-one. However, in order to most efficiently use cpu resources, modern superscalar processors actually begin executing many instructions in parallel. In cases where instructions depend on the result of previous instructions or checks which have not yet completed, execution happens based on guesses about what the outcome will be.
If the guess is correct, execution has been sped up. If the guess is incorrect, partially-executed instructions are cancelled and architectural state changes (to registers, memory, and so on) reverted; but the whole process is no slower than if no guess had been made at all. This is sometimes called “speculative execution”.
Unfortunately, although architectural state is rolled back, there are other side effects, such as changes to TLB or cache state, which are not rolled back. These side effects can subsequently be detected by an attacker to determine information about what happened during the speculative execution phase. If an attacker can cause speculative execution to access sensitive memory areas, they may be able to infer what that sensitive memory contained.
I had to check Wikipedia what TLB was:
A translation lookaside buffer (TLB) is a memory cache that is used to reduce the time taken to access a user memory location. It is a part of the chip’s memory-management unit (MMU). The TLB stores the recent translations of virtual memory to physical memory and can be called an address-translation cache.