What do the arrows in mechanisms represent?

The arrows represent the movement of a lone pair of electrons. For example, if a mechanism involves an oxygen atom forming a bond with a proton (hydrogen ion), then the oxygen would ‘donate’ a lone pair to the hydrogen ion and hence form an Oxyegn-Hydrogen bond.As electrons are negative, they are attracted to positives, and so the general rule of thumb is that the arrow starts at the negative and ends at the positive. Using our example above, oxygen is highly electronegative and so will have a strong delta - charge, and the hydrogen ion has a +1 charge, so the arrow starts at the oxygen (most negative) and ends at the hydrogen (most positive).