In this thesis, at first we study Verlinde’s approach to gravity which interprets gravitational interaction as a kind of entropic force. Then propose a model for the quantum bits of space-time on stretched horizon and holographic screens. A recent work by Verlinde has proposed a qualitatively new approach to gravity which joins the holographic and thermodynamic ideas. The essence of the approach is based on two principles: first is the holographic principle through which space is emergent. The holographic principle supposes that space is only a kind of container of information. The information is stored on holographic screens, which separate points. Also, the screens are equipotential surfaces. The second principle suggests that when the body moves relatively the screen it exerts an entropic force, similar to the one that appears in osmosis or when big colloid molecules are surrounded by thermal environment of smaller particles. Thus, according to the Verlinde approach, gravity is not a fundamental interaction like other three but a kind of entropic force. Whatever fantastic these ideas look like, they allowed to derive both the Newton law of gravity and the Einstein equations. Motivated by this new interpretation of gravity, we study equipotential surfaces, the Unruh-Verlinde temperature, energy, acceleration and . The physics of black holes attracted wide attention as an arena for study of statistical concepts like entropy. In this context the idea of a stretched horizon arose as a useful tool for thinking about black holes. Therefore, we consider a system with relativistic and non-interacting Bose particles located in a static space-time with horizon, like Rindler, Schwartzschild and general form of spherically symmetric static space-times. We merely know that the system is confined in a box with one dimension less than space. It is well known that theory of the grand canonical ensemble is sufficient to find all of the thermodynamical variables. At first we need to evaluate the density of state in the background of a curved space-time. It is shown that the gas on the stretched horizon is in a Bose-Einstein condensed state with the Hawking temperature, if the particle number of the system be equal to the number of quantum bits of space-times. Originally, we assuming that total number of particles are proportional to the area of the box. In the following, we evaluate another statistical quantity like entropy. One of excellent result is the entropy-area relationship of the stretched horizon. In this way, we may obtain the Bekenstein-Hawking entropy as well as its corrections which are somewhat universal in theories of quantum gravity such as string theory and loop quantum gravity. Also we evaluate that a boson gas on a holographic screen with the same number of particles and at Unruh-Verlinde temperature is also in a condensed state. Far from the horizon, the Unruh temperature is much lower than the condensation temperature. This analysis implies a possible physical model for quantum bits of space-time on holographic screen. It should be noted that this results is also valid for Kerr space-time. Keywords: Thermodynamics, Black Holes, Condensation, Stretched horizon, Holographic screen