What does it mean when a metal has a high specific heat? And what would be the effect in your value of specific heat if the metal was not left in the boiling water long enough to reach the temperature of the water

If a metal has a high specific heat it means that it takes a lot of energy to raise the temperature by one (1) degree C.

I don't know how you conducted your experiment but if you heated the metal in boiling water then transferred it to a container of water with a known (but cooler--say 25C) temperature, then measured the final T, think about this.
This is what should have happened.
mass metal --say 100g
Tinitial for metal = 100(boiling water)
Tfinal after mixing = say 39.5

mass H2O in container = 300 g
specific heat H2O = 4.18J
Initial H2O T = 25
Final T of metal and H2O = 39.5

Now suppose you allowed the metal to heat to 70 only before removing it from the boiling water. I worked it out and the final T will be 33.7. Now the numbers look like this. (Note Ti for the metal is 70 but you think it is 100).
[100*sp.h.*(33.7-100)] + [30*4.18*(33.7-25)] = 0
Solve for sp.h. of the metal. Compare with the value of 0.3 which you should have obtained if you had allowed the metal to heat to 100 C.