A type I error is when the null hypothesis is rejected when it is in fact true. The $p$-value gives the probability of doing this.
A roulette wheel may be unbiased but still land on red $10$ times in a row, even though the chance of this is extremely small, it is not impossible. If a hypothesis test was done on this data, it would reject the null hypothesis (that the roulette wheel is not biased) at a very low significance level, despite the fact that the roulette wheel is not biased. (In this case the $p$-value is $2^{-10}$ ).
A type II error is when the null hypothesis is accepted when it should not be.
This time, the roulette wheel is biased towards landing on red $75$% of the time. However when the test to check if it is biased is performed, we may observe that it lands on red $5$ times and black $5$ times. After performing a hypothesis test, we would see that we have obtained what is expected so the test statistic will not be in the critical region and hence we would accept the null hypothesis (that the roulette wheel is not biased) despite the fact that it is actually biased.