Magnesium is a vital nutrient for plants; among its other roles, it's essential in the production of chlorophyll, since each molecule of chlorophyll contains a magnesium ion. Adding magnesium sulfate (Epsom salt) can help remedy magnesium deficiencies. It does not affect pH.
Magnesium sulfate is an effective way to increase soil magnesium and sulfate content. Note, however, that if your plant already has the all nutrients it needs, adding more magnesium sulfate is unlikely to spur further growth. Only add magnesium sulfate if your plant is suffering from a deficiency.
Aqueous solutions of magnesium sulfate are neutral or only very slightly acidic and will have no effect on soil pH. Magnesium sulfate is a magnesium salt of sulfuric acid and as such is a neutral salt. Adding Epsom salt to soil will not reduce or increase pH, so it will not make the soil either more acidic or more basic.
It's best to test soil for pH, magnesium and/or sulfur content before adding Epsom salts. If the soil pH is low (as is often the case in magnesium-deficient soils), you may want to choose another fertilizer like dolomitic lime that will both add magnesium and increase soil pH. Many garden stores sell soil testing kits or may be able to test a soil sample for you.