determinism
Determinism is the property that, at every step, the machine has exactly one thing it can do — no choices, no coin flips, no branching. Reading a deterministic machine is like following a recipe with no 'either/or' steps: from where you are, the next move is forced. Run the same machine on the same input a thousand times and you trace the very same path every time.
Concretely, for a DFA determinism means the transition function δ gives back a single next state for each (state, symbol) pair: δ(q, a) is one state, never a set of options and never undefined. Two conditions together capture it: there is exactly one start state, and from each state every symbol leads to exactly one successor. That is the entire meaning of the 'D' in DFA.
It is worth being honest about what determinism does and does not buy you. It makes a DFA trivially easy to simulate — you just follow the single path — and it makes reasoning crisp. But determinism does not limit which languages a finite automaton can recognise: deterministic and nondeterministic finite automata recognise exactly the same class of languages (the regular languages). Nondeterminism, the opposite property where the machine may have several legal moves, is a convenience for description, not extra computational power, at the finite-automaton level.
In a DFA's transition table every cell holds exactly one state. If a single cell instead listed two states (say δ(q,a) = {p, r}), or some cell were blank, the machine would no longer be deterministic — it would be nondeterministic or simply ill-defined as a DFA.
Determinism: exactly one start state and exactly one successor per (state, symbol).
Determinism is not the same as predictability of the input. A DFA's behaviour is determined by the input it reads; given the input, no randomness remains — but it cannot foresee symbols it has not yet read.