the blank symbol
The blank symbol is the machine's way of saying 'nothing has been written here yet'. Because the tape is infinitely long but the input is only finitely long, every cell beyond the input must contain something, and that something is the blank. Think of it as the colour of empty notebook paper: present everywhere you have not yet drawn, and clearly different from any mark you might make.
Formally the blank is a special symbol, often written B or the box character, that belongs to the tape alphabet but is NOT part of the input alphabet. So at the start of a computation the tape holds the input string written in input symbols, with blanks filling every other cell, infinitely far in both directions of emptiness. The blank is what lets the machine detect the end of the input: when the head, scanning rightward across the input, first reads a blank, it knows it has run off the end. The machine may also write blanks of its own to erase cells back to emptiness.
The reason the blank must be excluded from the input alphabet is subtle but important: if a blank could appear inside the input, the machine could not tell the genuine end of the input from a blank that is part of it. By reserving the blank for 'empty', the model gets a clean, unambiguous boundary marker for free. The blank is one of several extra symbols, beyond the input letters, that the tape alphabet provides for the machine's bookkeeping.
For input alphabet {0, 1}, a tape alphabet might be {0, 1, X, B} where B is the blank. The tape for input 10 is ... B B 1 0 B B ..., so when the head moves right past the 0 and reads B, the machine concludes the input ended.
Blanks mark everything outside the input and serve as the end-of-input signal.
The blank is in the tape alphabet but never in the input alphabet. This exclusion is what gives the machine an unambiguous way to know where the finite input stops.