Its very hard to answer without more information. Generally the intercept isn't of much interest in a model, but there are exceptions. Its the expected value of the outcome Y when all predictors are zero. Usually that's not an interesting quantity and testing whether it is different from zero is also rarely of interest. So in most cases its fine, unless there is good reason to believe the intercept should not be zero or close to zero in this context.

If the multivariate model included the intercept term, the (intercept) term must be important. It is the expected response when all explanatory variables are each equal to zero. If not significantly different from zero, so be it.

Hello Supratim Guha

I think you better explain what your Y or Dependent Variable (DV) is before you ask for an explanation about X's and Intercept as well.

I think answering the question, what is DV or Response, helps us to know whether your MLR model is fundamentally correct or not.

Probit, Logit, Multinomial, Ordinal, Quantile, Poisson, .....

They are all standing behind the door for you to call them