A small p-value means that there is strong evidence against the null hypothesis. But a large p-value does not mean that is true.
The p-value is commonly compared to a cut-off value of 0.05, called significance-level. The cut-off point should be decided on before the data is collected and analysed.
Critical values are cut-off values that define regions where the test statistic is unlikely to lie. […] The null hypothesis is rejected if the test statistic lies within this region which is often referred to as the rejection region(s).
– 188.8.131.52. Critical values and p values – NIST