In addition to @DaveT's helpful answer, here are a few more clarifications regarding the estimated intercepts in your models.
Model 1
The (true) intercept in your first model
lm(mpg ~ 1, data=mtcars)
represents the mean value of mpg for all cars represented by the ones included in this data set, regardless of their displacement (disp) or horse power (hp). In this sense, the (true) intercept is simply the unconditional mean of mpg. Based on the data, its value is estimated to be 20.091.
Model 2
The (true) intercept in your second model:
lm(mpg ~ disp, data=mtcars)
represents the mean value of mpg for all cars represented by the ones included in this data set which share the same displacement (disp) value of 0. This intercept is estimated from the data to be 29.599855. Because displacement is a measure of the engine size of a car, it doesn't make sense that you would have a car with a displacement of 0, suggesting that the intercept interpretation in this model is meaningless in the real world.
To get a meaningful interpretation for the intercept in your second model, you could center the disp variable around its observed mean value in the data (presuming disp has an an approximately normal distribution) and re-fit the model:
disp.cen <- mtcars$disp - mean(mtcars$disp)
lm(mpg ~ disp.cen, data=mtcars)
In the re-fitted second model, the intercept will represent the mean value of mpg for all cars represented by the ones included in this data set which have a "typical" displacement (disp). Here, a "typical" displacement means the average displacement observed in the data.
Model 3
The (true) intercept in your third model:
lm(mpg ~ disp + hp, data=mtcars))
represents the mean value of mpg for all cars represented by the ones included in this data set which share the same displacement (disp) value of 0 and the same horse power (hp) value of 0. This intercept is estimated from the data to be 30.735904. Because displacement is a measure of the engine size of a car and horse power is a measure of the engine power of a car, it doesn't make sense that you would have a car with a displacement of 0 and a horse power of 0, suggesting that the intercept interpretation in this model is meaningless.
To get a meaningful interpretation for the intercept in your third model, you could center the disp variable around its observed mean value in the data (presuming disp has an an approximately normal distribution), center the hp variable around its observed mean value in the data (presuming hp has an an approximately normal distribution), and then re-fit the model:
disp.cen <- mtcars$disp - mean(mtcars$disp)
hp.cen <- mtcars$hp - mean(mtcars$hp)
lm(mpg ~ disp.cen + hp.cen, data=mtcars))
In the re-fitted third model, the intercept will represent the mean value of mpg for all cars represented by the ones included in this data set which have a "typical" displacement (disp) and a "typical" horse power (hp). Here, a "typical" displacement means the average displacement observed in the data, whereas a typical horse power means the average horse power observed in the data.