Cryptography describes the science and methods we can use to mathematically obscure (and in some cases de-obscure) information. The way this plays out in practice of course has a lot of nuance to it, but as we're all aware the main process for doing this is to take some data and perform calculations on it that are essentially impossible to undo. (Of course, in theory, they can be performed in reverse, but thanks to minor constraints like thermodynamics that's not actually feasible or, for any relevant purpose, possible.) These calculations can be performed on a character-by-character basis using a design known as a stream cipher. The alternative is to take the input data, break it into chunks (blocks), and perform calculations on the blocks. This design is known as a block cipher.
Given the nature of your question, I'm sure this is all information you already have, but I think it's worth outlining for future readers.
To answer your question, larger blocks are safer for the same reason that cryptographic algorithms use things like modulus functions and elliptic curve tangents: intricacy. All of these elements are incredibly complex on their own, and put together form a system that essentially represents a hardened web of computations. In the case of block size in specific, each added bit presents a new multiplier of potential values, increasing the difficulty in guessing the contents of that bit. No matter how hard you try, a 2 bit block, spun round and round and calculated on in circles, is going to show patterns over time, no matter how good the underlying algorithm is. These patterns show seams and the encryption can be cracked.
A 128 bit block, on the other hand, is much harder to guess. For one, it's difficult to guess the contents of that block on its own, even in cleartext.
But given a cryptographically secure algorithm, it is feasibly impossible to crack a 128 bit block. Good luck spotting patterns, and you're definitely not going to get any collisions there.
Another way to think of it is simply as layered security. Larger blocks present more layers of data for your encryption function to use, and that produces more layers of encryption at the end.