When two colorless solutions are mixed, bubbles being formed indicate the production of a gas that was not present before mixing the solutions. This gas is most likely the result of a chemical change or chemical reaction. A chemical change is one in which the atoms present before the change are rearranged and one or more new substances is produced. The substances present before the change are called reactants. The bonds of the reactant particles are broken. The atoms are then rearranged and new bonds form creating new substances.
"Give two possible explanations for this" is very open ended and without a context, I can only guess at what the question is meaning. Two explanations might include two sets of colorless solutions that might yield a gas. What comes to mind is the production of carbon dioxide which could come from a soluble carbonate, such as sodium carbonate solution, and an acid, such as vinegar or hydrochloric acid. A second possibility is a gas such as ammonia. This could be produced by the reaction of a soluble ammonium compound, such as ammonium chloride, and a base such as sodium hydroxide.
Hope that helps.