Laplace smoothing is a way to move probabilities towards uninformed mean. Suppose you have a multinomial variable with sample counts $c_1, c_2,..,c_d$, where $d$ is the number of dimensions. A Laplace smoothed version of estimated probabilities has the form: $(c_i + \alpha)/(N + d\alpha)$, where $\alpha$ is positive. If $\alpha$ is $0$ then we have non smoothed estimator. Often $1$ is used to solve the problem of missing categories. But values greater then one can be used. If large values are used than the influence of observed counts will be lower because estimated probabilities for the same number of observations will be lower. A direct consequence is that the variance of the model (estimates) is lower, possibly with larger bias. You can see the value of $\alpha$ as the strength of a Bayesian uninformed prior.
Suppose you $d=2$, and you have a training dataset with a single example, of the first category. Using Laplace smoothing with $\alpha=1$ we would estimate the probabilities as $0.66, 0.33$ If use $\alpha=10$ we get $0.52,0.48$, much closer to equal probabilities $0.5,0.5$