A model that estimates probabilities by counting assigns zero to everything it has not seen, and that is serious. The unseen is the norm: nearly half the words in a corpus occur only once (Witten et al., 2017, p. 516). And zeros are contagious: in Naive Bayes, a zero probability "holds a veto" over all the others (2017, p. 99); in an n-gram model, a single unseen sequence wipes out the probability of the whole sentence. Smoothing means taking some probability away from the observed and spreading it over the unobserved.
Tiny example. If the sky was sunny, overcast and rainy on 2, 4 and 3 of 9 days, the frequencies are 2/9, 4/9 and 3/9. The Laplace estimator adds 1 to each count and 3 to the denominator: 3/12, 5/12 and 4/12. In general one estimates (n + μp)/(N + μ), where p is a prior probability and μ sets how much it weighs against the evidence; this amounts to taking the posterior mean under a Dirichlet prior (2017, pp. 99–100).
With large vocabularies, adding one steals too much mass from what was seen; n-gram models used finer methods. Back-off falls back on a shorter context when the longer one never occurred, and interpolation mixes several orders (Bengio et al., 2003, p. 1138); around 2003, modified Kneser–Ney was the strongest (2003, p. 1148).
In a network, the softmax never outputs zero, and since similar words have similar vectors, seeing The cat is walking in the bedroom also raises the probability of A dog was running in a room (Bengio et al., 2003, pp. 1139–1140): the representation now does the smoothing. A deliberate echo remains: the Transformer was trained against slightly blurred targets (label smoothing), which hurts perplexity but improves BLEU (Vaswani et al., 2017, sec. 5.4).
Smoothing is the quantitative version of a problem of induction: how much to trust observed frequencies and how much what was expected beforehand (inductive bias). Assigning zero to the never-seen is dogmatism: no evidence could ever correct it.