The intercept-only model looks like this in R:
m0 <- glm(dichotomous.outcome.variable ~ 1,family = binomial(link = "logit")), data = data)
and stipulates that the probability of success (where success means that dichotomous.outcome.variable = 1) is constant - in particular, it does not depend on any of your measured predictor variables.
The model which includes the age and hpv predictors looks like this:
m1 <- glm(dichotomous.outcome.variable ~ age + hpv,family = binomial(link = "logit")), data = data)
and stipulates that the probability of success depends on both age and hpv (e.g., probability of success might increase with age but decrease with hpv).
When you compare the two models, you are essentially testing two competing hypotheses:
Ho: probability of success is constant
Ha: probability of success depends on both age and hpv
If Ho is true, a subject's age and hpv have no bearings on his/her probability of success. If Ha is true, a subject's probability of success would be influenced by their age and hpv (e.g., an old subject with a low hpv value would have a high probability of success), though the influence of age on this probability is independent of hpv and viceversa.
One way you can test these mutually exclusive hypotheses is by examining the reduction in null deviance achieved by introducing the age and hpv predictors in the intercept-only predictor. If the reduction is (statistically) significant, the data provide evidence against the null hypothesis of constant probability of success and in favour of the alternative hypothesis on non-constant probability of success which depends on age and hpv.
Thus, it is not enough to merely compute the reduction in null deviance, you must also determine if this reduction is statistically significant. See
Interpreting Residual and Null Deviance in GLM R for how you might do that. Alternatively, just compare your two model fits above with the anova function:
anova(m0, m1, test = "Chisq")
The PLoS One article Non-significant p-values? Strategies to understand and better determine the importance of effects and interactions in logistic regression by Vakhitova et al. (doi:10.1371/journal.pone.0205076) will give you a more comprehensive look at the issue discussed in my answer: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6261058/.