Most likely somebody is using this phrase to say "to try out" or "to give it a chance". For example, "I have never went mountain biking before but I am will to take a run at it." or "I am new to these lessons but they may be worth taking a run at.". The act of physically running is not necessarily related to this phrase but is being used in a different meaning. Sometimes you will see similar phrases such as "I will give it a go" or "It is worth a shot".
Professional Online Language Teacher from USA, Jeanne