Implicit (continuum) solvation is a method to represent solvent as a continuous medium (solvent molecules are replaced by a homogeneously polarizable medium) instead of individual “explicit” solvent molecule. The main parameter used to represent the solvent is the dielectric constant (ε). Explicit models
consider molecular details of each solvent molecule.
The implicit solvation model is justified in liquids, where the potential of mean force can be applied to approximate the averaged behavior of many highly dynamic solvent molecules. However, the interfaces and the interiors of biological membranes or proteins can also be considered as media with specific solvation or dielectric properties. These media are not necessarily uniform, since their properties can be described by different analytical functions, such as “polarity profiles” of lipid bilayers. There are two basic types of implicit solvent methods: models based on accessible surface areas (ASA) that were historically the first, and more recent continuum electrostatics models, although various modifications and combinations of the different methods are possible.
Explicit solvent models treat explicitly (i.e. the coordinates and usually at least some of the molecular degrees of freedom are included) the solvent molecules. This is a more intuitively realistic picture in which there are direct, specific solvent interactions with a solute, in contrast to continuum models. These models generally occur in the application of molecular mechanics (MM) and dynamics (MD) or Monte Carlo (MC) simulations, although some quantum chemical calculations do use solvent clusters. Molecular dynamics simulations allow scientists to study the time evolution of a chemical system in discrete time intervals.
Explicit solvation models explicitly take into account each individual atom (i.e. the coordinates and usually some of the molecular degrees of freedom are included).
More parameters are used to model the atoms resulting in more accuracy.
Hydrogen bond, hydrophobic interaction, and viscosity are taken into account.
Computationally more expensive.
More commonly associated with Quantum mechanics.
Implicit solvation models (also known as continuum solvation model) uses approximation/averaging instead of modeling all atoms thus, treating the solvent as a continuum rather than discrete atoms.
A small number of parameters are used, the most important one being the dielectric constant (ε) (less accurate).
Computationally more efficient/ less resource-intensive.
Hydrogen bond, hydrophobic interaction, and viscosity are not taken into account.
GBSA [Generalized Born (GB)/surface area (SA)] is one of the most commonly used implicit solvent models.
More commonly associated with Molecular dynamics.
There is a third model, aptly named Hybrid models; as the name suggests, is in the middle between explicit and implicit models. Quantum mechanics and molecular mechanics models,(QM/MM) schemes, can be thought of in this context.
QM/MM methods enable a part of the system to be calculated using quantum mechanics (think explicit solvation), for example, the active site in a biological molecule, whilst the rest of the system is modeled using MM force fields (think implicit solvation).
@Maruf Ahmed has explained well. The answer is very simple and clear. Both implicit and explicit solvation models are being used during computational studies. In explicit account of solvation environments, simulating a large number of solvent molecules and performing sufficient sampling to achieve converged thermodynamic properties are still largely intractable, even numerically most efficient approaches like DFT in combination with lowering exchange-correlation functionals.
In this situation, implicit solvation methods enjoy a long-standing popularity.