On molecular scales, higher temperature is faster motion. As with all objects, faster movement corresponds to higher kinetic energy. Higher kinetic energy allows more energy transfer into electrons upon collision, and therefore a higher probability a molecule collision will reach a reaction's activation energy. A ubiquitous case of chemical kinetic principles put to use is refrigeration. Cooling food proportionately decreases the probability a molecule pair will have energy to undergo the reactions that spoil food. Note that refrigeration does not categorically prevent spoilage; the process is merely slowed.
The reaction rate equation is a function of reactant concentration. In single-step reactions---reactant R to product P---only R and P concentrations are relevant. In multistep reactions, things are a bit more subtle. Reactant R---intermediate I---product P processes may depend on concentrations of "I." Intermediate(s) may exist fleetingly, disappearing in the course of reactions. Therefore, their concentrations would remain unknown and confound expectations based on simpler chemical kinetics models. Concentration does not affect activation energy. Concentration increase corresponds to more instances in which the same activation energy is achieved in a certain time period.
If a reactant is in the solid phase, kinetic dynamics change. Since a surface exposes a portion of reactant molecules, the molecules available for potential reaction effectively decrease. Surface area/volume is not the only change in molecules available for reactions. Atoms in solid phases require certain energy to break from the bulk of the substance. For instance, when salt dissolves, the hydration shell forming around a surface sodium (or chloride) atom must have enough attraction to overcome the bonding energy of the nondissolved sodium chloride crystal lattice.
Catalysts are relevant to chemical kinetics since they increase reaction rate without changes in temperature, concentration or reactant phase. These substances do not react but facilitate reactions. Catalysts exist as homogenous (same phase) or heterogeneous (different phase) with respect to reactants. Note that the catalyst effect can be circumscribed by concentration and temperature indirectly. A small catalyst amount can interact with a limited and proportionately small amount of reactant particles in a given time period. In rate equations, the catalyst effect is usually implicit in a higher rate constant (k) value.
Chemical kinetics approximates molecules as pointlike or spherical for an initial conceptual explanation. Greater accuracy and fidelity to experimental evidence is attained by considering molecule geometry. The V-shape of water molecules means electron density, collision energy distribution and probability of conversion to product (or intermediate) depends on what portion of the "V" is struck by another molecule. Reaction rate equations do not explicitly capture molecular geometry.