There are two different ways to conceive of this question, each with a different answer.
One way to understand this question is to say that it is asking about our conscious choices. In other words, how much do we think about economics on a day to day basis? For most people, the answer would be very little. Most people do not think much about things like opportunity costs or supply and demand when they are making decisions in their everyday lives. Therefore, for the vast majority of people, economics plays a very small conscious role in their lives.
But there is another way to understand this question. The question could be asking about the impact of economics on our lives even when we are not conscious of that role. In this case, the answer would be much different. Economics plays a huge unconscious role in our lives. Let us look at two ways in which this is so.
Economics plays a large role in our own choices. Every time we make a decision to buy something, we are making an economic decision. Once we spend that money, it cannot be spent on anything else (because of scarcity). Therefore, when I buy a gallon of milk, I am giving up the chance to buy anything else with that $2.60 (opportunity cost). I am also making the unconscious decision that the utility I get from the milk is greater than the utility I would get from using the $2.60 in some other way.
Economics also shapes the world in which we live. Our salaries are determined largely by supply and demand. The prices of the things that we buy are determined by supply and demand. The strength of our economy, which helps determine whether we will be able to get and keep jobs, depends on a variety of macroeconomic factors.
Therefore, although we are not always aware of it, economics shapes our lives in many important ways.