It is true from the absolute perspective that what we are living in a dream. The problem is, at this point, the world is very real to us because our ignorance of Reality. As long as it feels real, we must play by the rules of the game. From the absolute perspective, rightly, you will ask what is the point of giving our best if everything we see around us is a dream. The point is how do we get out of this dream.
Vedanta tells us that the way out of the dream is to reduce our desires and eventually eliminate them. Our desires can be reduced by following the three yogas prescribed by Vedanta i.e. karma yoga (the path of action), bhakti yoga (the path of devotion) and jnana yoga (the path of knowledge). Karma yoga is acting in a spirit of service and sacrifice, dedicating our actions towards a higher, selfless ideal. Bhakti yoga is the process of purifying our emotions, of being able to see the unity in the diversity. Jnana yoga is the process of constant discrimination between the changing, transitory world and the unchanging, permanent substratum of Divinity underlying the world.
You ask why should we give our best in spite of this being a dream. This is directly related to karma yoga, the path of action. Karma yoga is about converting our actions into acts of worship. And our actions can become worshipful only if we act wholeheartedly by giving our best. They become worshipful only when we consider whatever we do as sacred, treat it as an offering to that higher Power that has bestowed us with the ability to act. This is why we are urged to give our best to anything we undertake, whether it is a small errand to be run or a large strategising operation at the workplace. Every act must be converted into one of worship.