Let me start from the basics, Distillation is used to purify a mixture that has volatile liquid and non-volatile impurities.
We use Steam distillation in which the oil has a significantly high boiling point than water atleast and it is also immiscible with water.
1)Steam does not increase its external pressure rather it increases the mixture's vapor pressure as well as partial pressure due to water vapor. What happens is that the steam which we pass into the oil makes a mixture with the oil and creates an oil-water mixture which is an azeotrope, so now the water in the oil-water mixture has its own vapor pressure which is now added to the vapor pressure of oil, which increases the mixture's internal pressure.
2)As I have said earlier, the oil-water mixture is an azeotrope, so the boiling point of the mixture becomes significantly less than the boiling point of the oil.
For example, by data for Pehnylaniline and water mixture, saturation pressure of phenylaniline is 7.07 kPa and for water, it is 94.30 kPa and hence for the mixture, it is 7.07 + 94.30 = 101.37kPa and hence the mixture will boil just below 100-degrees Celcius but if we take Phenylanline only then its boiling point is 184-degree Celcius which makes it easier to carry out distillation.
Also, we use steam to provide heat to the oil-water mixture. The steam provides heat to the oil by condensing which also reduces its loss to the flask, environment, etc.
Some links for sources,
Steam distillation- how it actually works?
Internal vs external steam distillation