Imperfection means a situation where there is some flaw or limitation which cannot be improved and hence people have to live with that situation. Markets or financial markets in particular are never perfect, in stock markets it is assumed that all information is in public domain and therefore the price of stock reflects the true value of the stock. However there are always group of people who have more information than others and therefore they take advantages on the basis of that information which in turn makes the financial markets imperfect as the basic premise of any perfect market is that nobody should take undue benefit of other parties due to additional information which he or she has.
It can better explained with the help of an example, suppose you are an accounting head of a company which is listed in markets and since you have all the information regarding the accounts of the company you will also know the profit or loss which the company has made during a particular quarter. If a company has made profits in excess of estimates than we all know on publishing of results the stock price of that company reacts positively, since you as an accountant know these numbers before anybody else you have more information than others and therefore you can take advantage of that information. There are many rules and regulations which the stock exchanges all over the world has put in order to curb such practices, but still these type of instances happen where an individual or group of individuals take benefit of market inefficiencies.
Another example would be in case of real estate market where the person who is a local or who is living in a particular area for past many years has more knowledge about the prices of land than a person who is new to that area. Now if both the persons deal with each other than naturally the person who is having more information would take advantage of other party making it a market imperfection.